What is a Logic?

Till Mossakowski (), Joseph Goguen (), RĂzvan Diaconescu () and Andrzej Tarlecki ()
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Till Mossakowski: Universität Bremen
Joseph Goguen: University of California at San Diego
RĂzvan Diaconescu: Romanian Academy, Institute of Mathematics
Andrzej Tarlecki: Warsaw University, Institute of Informatics

A chapter in Logica Universalis, 2005, pp 113-133 from Springer

Abstract: Abstract This paper builds on the theory of institutions, a version of abstract model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual. A natural equivalence relation on institutions is defined such that its equivalence classes are logics. Several invariants are defined for this equivalence, including a Lindenbaum algebra construction, its generalization to a Lindenbaum category construction that includes proofs, and model cardinality spectra; these are used in some examples to show logics inequivalent. Generalizations of familiar results from first order to arbitrary logics are also discussed, including Craig interpolation and Beth definability.

Keywords: Universal logic; institution theory; category theory; abstract model theory; categorical logic (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7304-7_7

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DOI: 10.1007/3-7643-7304-0_7

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